Rat are believed to have a dry bite because their incisors are so
far foward in the mouth that they don't get coated with saliva.
Therefore, rats are believed to be incapable of transmitting
saliva-borne diseases.

The dry bite hypothesis is usually mentioned in the context of
rabies transmission: rats are believed to be incapable of
transmitting rabies (a saliva-borne disease) because of their dry
bite.

Do rats have a dry
bite?

No. The rat dry bite idea is a myth. Rats have a wet bite and can
transmit saliva-borne diseases. Here's the evidence:

Rats transmit saliva when they bite

Wong et al. (1984) report a case of a patient who developed
a swelling around the site of a rat bite. Later allergy testing on
the patient's skin showed that the patient had a rare allergy to rat
saliva and to chemicals found in the saliva of the rat that bit him.
These allergy tests show that the rat's bite transmitted saliva to
the patient.

Rabies from rats is very rare and has never been documented in the
United States. However, a handful of cases of rabies from a rat bite
have been recorded in Poland (Zmudziñski and Smreczak 1995,
described in Wincewicz 2002), Israel (Gdalevich et al. 2000),
Thailand (Kamoltham et al. 2002) and Surinam (Verlinde et
al 1975).

Contracting one of these diseases from a rat bite is a rare
occurence, but the fact that it can occur shows that rats can
transmit saliva-borne diseases.

If foward-placed incisors make a bite dry, then other species with
forward-placed incisors (e.g. other rodent species, rabbits) should
have a dry bite too and should also be incapable of transmitting
saliva-borne diseases or causing humans to have an allergic reaction
to their saliva.

Rats do not have a dry bite: they can transmit saliva when they
bite. Rats therefore can, and do, transmit saliva-borne diseases.
These diseases are rare, but the fact they are transmitted refutes
the dry-bite hypothesis.

As the dry bite hypothesis usually comes up in the context of
rabies tramsmission, note that rats almost never carry rabies and are
not considered a serious rabies risk. Rabies transmission from rats
is extremely rare, not because rats have a dry bite, but because they
almost never carry rabies, presumably because rats do not survive the
attack of a rabid animal.

Lastly, the term dry bite is a real term. It refers, not to
a "salivaless" bite, but to a bite without venom from a venomous
animal such as a rattlesnake or a spider.